Minimum Variance Quadratic Unbiased Estimation Research Articles

On Estimating Variance Components of Two-Way Nested Random Model with Missing Information

In this paper, the estimators of variance components are derived of two-way nested random model when the problem of missing information exists using combination between Modified Minimum Variance Quadratic Unbiased Estimation (MMIVQUE) and Modified Minimum Variance Quadratic Unbiased Estimation (MMIVQUE (0)) methods that is called MMIV(MIV(0)) method.

Variance component estimators OPE, NOPE and AOPE in linear mixed effects models

SummaryOptimum variance component estimation methods that yield uniformly minimum variance quadratic unbiased estimators for a full dataset are often difficult or impossible to implement. In this paper we propose an estimator which is near optimal under some distributional assumptions that can be made without specifying an exact functional form. This estimator has an exact closed form expression. An average optimum estimator, which can be used when optimum estimators exist for subsets of the data, is also proposed. Performance comparisons of the proposed estimators are made individually with other popular estimators using simulated data. A performance comparison of the average optimum estimator is made under four constraints on the variance components. A real dataset is analysed using the proposed estimators. The robustness properties of the proposed estimators, in comparison with the other estimators, including the method of moments, are also investigated, using data simulated from a skew normal distribution. The average optimum estimator is strongly robust and far superior for estimating one of the variance components, as demonstrated by making comparisons with other methods. These comparisons are based on bias, mean squared error, and mean absolute deviation. The average estimator is moderately robust in respect of the estimation of the other variance components.

Comparison and robustness of the REML, ML, MIVQUE estimators for multi-level random mediation model

ABSTRACTThis article concentrates on the multi-level random mediation effects model (1-1-1) and reviews the maximum likelihood (ML), restricted maximum likelihood (REML), and minimum variance quadratic unbiased estimation (MIVQUE) estimation methods provided by the SAS MIXED process. This paper uses Monte Carlo simulation to make a comparison of the performance of these estimators under a wide variety of different conditions. First, REML and ML produced equivalent results and both of them outperformed MIVQUE, no matter whether the normality assumption was satisfied. Second, the results indicated that the distribution of the does not influence the mediation effect. The deviation of the normal distribution of or ‘ and ’ affected the mediation effect, particularly in condition that not only the magnitude of the deviation but also the covariance between these two effects were large. This thesis ends with the implications, suggestions and recommendations for the application.

On modified minimum variance quadratic unbiased estimation (MIVQUE) of variance components in mixed linear models

The present paper deals with some modifications on the computational aspects of MIVQUE of variance components in mixed linear models. As a result two modified MIVQU estimators namely (MIVQUE I and MIVQUE II) are introduced. Further the relative performances of Modified MIVQU estimators are assessed with that of Mitra Type Estimators (MTE) and MIVQU estimators for unbalanced one way random model based on different optimality criteria with various n- patterns.

Heritability and Variance Component Estimates of Meat Quality in Japanese Quail (Coturnix coturnix japonica)

A comparison of 3 methods for variance component estimation to compute the heritability of meat quality characteristics (body weight, breast meat weight, breast yield, l, a, b, c, h, and ph) was performed using the methods of maximum likelihood (ML), restricted maximum likelihood (REML), and minimum variance quadratic unbiased estimator (MIVQUE). The parent population was set up at random from a closed population of Japanese quail (Coturnix coturnix japonica). Selection was not applied for any productive characteristics and no special care was taken to avoid inbreeding. After 12-h feed withdrawal, the birds were weighed and slaughtered at 35 days of age. Their carcasses were dissected. Then 24-h postmortem and breast meat (pectoralis major and pectoralis minor) weights (BRW) were measured. Ultimate pH values (pHu) of the left breast meat were measured with a pH meter (Hanna Instrument Model 8314) using a penetration electrode (FC-200) after 24 h post-mortem. Color measurements (brightness ´´l´´, redness ´´a´´, yellowness ´´b´´, chroma ´´c´´, and hue ´´h´´) of the left breast meat were carried out using a Minolta CM508d spectrocolorimeter connected to a computer. Heritabilities of meat quality characteristics estimated by maximum likelihood (ML), restricted maximum likelihood (REML) and minimum variance quadratic unbiased estimation (MIVQUE) ranged from moderate to high.

Estimation of Variance Components for a Linear Toeplitz Model

The linear Toeplitz covariance structure model of order one is considered. We give some elegant explicit expressions of the Locally Minimum Variance Quadratic Unbiased Estimators of its covariance parameters. We deduce from a Monte Carlo method some properties of their Gaussian maximum likelihood estimators. Finally, for small sample sizes, these two types of estimators are compared with the intuitive empirical estimators and it is shown that the empirical biased estimators should be used.

Minimum Variance Quadratic Unbiased Estimation for the Variance Components in Simple Linear Regression with Onefold Nested Error

The explicit forms of the minimum variance quadratic unbiased estimators (MIVQUEs) of the variance components are given for simple linear regression with onefold nested error. The resulting estimators are more efficient as the ratio of the initial variance components estimates increases and are asymptotically efficient as the ratio tends to infinity.

Estimation of Variance Components and Heritabilities of Growth Characteristics in Morkaraman Lambs Using Different Statistical Methods

Bilgin, O.C., Esenbuga, N., Macit, M. and Karaoglu, M. 2004. Estimation of variance components and heritabilities of growth characteristics in Morkaraman lambs using different statistical methods. J. Appl. Anim. Res., 26: 83–88. Henderson's method 3, maximum likelihood (ML), restricted maximum likelihood (REML) and minimum variance quadratic unbiased estimation (MIVQUE) methods were used to estimate variance components and to predict heritabilities of birth weight, weaning weight and daily weight gain until weaning in Morkaraman lambs. The different variance components methods gave similar results. The moderately-high estimate of heritability for weaning weight, demonstrates an opportunity for improvement of this trait through genetic selection.

Unbiased variance estimation in a simple exponential population using ranked set samples

The problem considered in this paper is that of unbiased estimation of the variance of an exponential distribution using a ranked set sample (RSS). We propose some unbiased estimators each of which is better than the non-parametric minimum variance quadratic unbiased estimator based on a balanced ranked set sample as well as the uniformly minimum variance unbiased estimator based on a simple random sample (SRS) of the same size. Relative performances of the proposed estimators and a few other properties of the estimators including their robustness under imperfect ranking have also been studied.

OPTIMAL QUADRATIC UNBIASED ESTIMATION FOR MODELS WITH LINEAR TOEPLITZ COVARIANCE STRUCTURE

This paper deals with the problem of quadratic unbiased estimation for models with linear Toeplitz covariance structure. These serial covariance models are very useful to modelize time or spatial correlations by means of linear models. Optimality and local optimality is examined in different ways. For the nested Toeplitz models, it is shown that there does not exist a Uniformly Minimum Variance Quadratic Unbiased Estimator for at least one linear combination of covariance parameters. Moreover, empirical unbiased estimators are identified as Locally Minimum Variance Quadratic Unbiased Estimators for a particular choice on covariance parameters corresponding to the case where the covariance matrix of the observed random vector is proportional to the identity matrix. The complete Toeplitz-circulant model is also studied. For this model, the existence of a Uniformly Minimum Variance Quadratic Unbiased Estimator for each covariance parameter is proved.

A comparative study of alternative estimators for the unbalanced two‐way error component regression model

Summary This paper considers the unbalanced two-way error component model studied by Wansbeek and Kapteyn (1989). Alternative analysis of variance (ANOVA), minimum norm quadratic unbiased and restricted maximum likelihood (REML) estimation procedures are proposed. The mean squared error performance of these estimators are compared using Monte Carlo experiments. Results show that for the estimates of the variance components, the computationally more demanding maximum likelihood (ML) and minimum variance quadratic unbiased (MIVQUE) estimators are recommended, especially if the unbalanced pattern is severe. However, focusing on the regression coefficient estimates, the simple ANOVA methods perform just as well as the computationally demanding ML and MIVQUE methods and are recommended.

Estimadores de componentes de variância em delineamento de blocos aumentados com tratamentos novos de uma ou mais populações

O objetivo do trabalho foi comparar, por meio de simulação, as estimativas de componentes de variância produzidas pelos métodos ANOVA (análise da variância), ML (máxima verossimilhança), REML (máxima verossimilhança restrita) e MIVQUE(0) (estimador quadrático não viesado de variância mínima), no delineamento de blocos aumentados com tratamentos adicionais (progênies) de uma ou mais procedências (cruzamentos). Os resultados indicaram superioridade relativa do método MIVQUE(0). O método ANOVA, embora não tendencioso, apresentou as estimativas de menor precisão. Os métodos de máxima verossimilhança, sobretudo ML, tenderam a subestimar a variância do erro experimental (<img SRC="http:/img/fbpe/pab/v36n9/6475s2.gif">) e a superestimar as variâncias genotípicas (<img SRC="http:/img/fbpe/pab/v36n9/6475s1.gif">), em especial nos experimentos de menor tamanho (n<120 observações). Quando as progênies vieram de um só cruzamento, REML praticamente perdeu estes vícios nos experimentos maiores e com razões <img SRC="http:/img/fbpe/pab/v36n9/6475s2.gif">/<img SRC="http:/img/fbpe/pab/v36n9/6475s1.gif">>0,5. Contudo, o método produziu as piores estimativas de variâncias genotípicas quando as progênies vieram de diferentes cruzamentos e os experimentos foram pequenos.

NONNEGATIVE ESTIMATORS FOR THE ONE-WAY RANDOM EFFECTS MODEL

The relative merits of ten estimators for the variance component of the balanced and unbalanced one-way random effects models are compared. Six of the estimators are nonnegative, two of which are obtained by modifying the Minimum Variance Quadratic Unbiased Estimator (MIVQUE) and the Weighted Least Square Estimator (WLS), and two more from the positive parts of these estimators. The Minimum Norm Quadratic Estimator (MINQE), which is nonnegative, is adjusted for reducing its bias. The nonnegative Minimum Mean Square Error Estimator (MIMSQE), the Analysis of Variance (ANOVA) and Unweighted Sums of Squares (USS) estimator are also included.

Minimum variance quadratic unbiased estimators as a tool to identify compound normal distributions

We derive the minimum variance quadratic unbiased estimator (MIVQUE) of the variance of the components of a random vector having a compound normal distribution (CND). We show that the MIVQUE converges in probability to a random variable whose distribution is essentially the mixing distribution characterising the CND. This fact is very important, because the MIVQUE allows us to make out the signature of a particular CND, and notably allows us to check if an hypothesis of normality for multivariate observations y 1,…, y M is plausible.

Covariance matrix minimum variance quadratic unbiased estimation for the MANOVA model

For the usual MANOVA model , Khatri (1979) obtained necessary and sufficient conditions for to be the minimum variance quadratic unbiased estimator of tr ... [sigma]. This paper uses Theil's (1968) BLUS procedure to construct an equally efficient quadratic unbiased estimator of tr ... [sigma].

MIVQUE and REML Estimators of Variance Components under Proportionality Condition

In this study, a one-way random effect model with unequal cell variances is considered, and the Minimum Variance Quadratic Unbiased Estimator (MIVQUE) and Restricted Maximum Likelihood (REML) estimator of the variance components are studied. The algebraic inversion of the variance matrix of the observation vector is obtained to achieve some computational convenience. Using the proportionality condition described by Talukder (1992) that the cell sizes are proportional to the cell variances, MIVQUE and REML estimators are shown to be the same as the ANOVA estimators.

MIVQUE and REML Estimators of Variance Components under Proportionality Condition

In this study, a one-way random effect model with unequal cell variances is considered, and the Minimum Variance Quadratic Unbiased Estimator (MIVQUE) and Restricted Maximum Likelihood (REML) estimator of the variance components are studied. The algebraic inversion of the variance matrix of the observation vector is obtained to achieve some computational convenience. Using the proportionality condition described by Talukder (1992) that the cell sizes are proportional to the cell variances, MIVQUE and REML estimators are shown to be the same as the ANOVA estimators.

The three-fold nested random effects model

Estimation of the variance components and the mean of the balanced and unbalanced threefold nested design is considered. The relative merits of the following procedures are evaluated: Analysis of variance (ANOVA), maximum likelihood (ML), restricted maximum likelihood (REML), and minimum variance quadratic unbiased estimator (MIVQUE). A new procedure called the weighted analysis of means (WAM) estimator which utilizes prior information on the variance components is proposed. It is found to have optimum properties similar to the REML and MIVQUE, and it is also computationally simpler. For the mean, the overall sample average, grand mean, unweighted mean, and generalized least-squares (GLS) estimator with its weights obtained from the above estimators for the variance components are considered. Comparisons of the above procedures for the variance components and the mean are made from exact expressions for the biases and mean square errors (MSEs) of the estimators and from empirical investigations.

Non-iterative robust estimators of variance components in within-subject designs.

Classic estimators of variance components break down in the presence of outliers and perform less efficiently under non-normality. In this article I present simple non-iterative estimators of variance components that are resistant to outliers and robust to systematic departures from normality, such as heavy tailedness of the distribution of responses. The proposed estimators are based on a robust extension of Hocking's AVE approach and are thus called RAVE estimators. I present results from a Monte Carlo comparison of RAVE versus classic estimation methods including maximum likelihood (ML), restricted maximum likelihood (REML) and minimum variance quadratic unbiased estimation (MIVQUE). Under simulated deviations from normality, RAVE estimators are associated with smaller mean squared errors than all the comparators, and in the normal case they exhibit a minimal loss in relative efficiency. A numerical example illustrates the proposed methodology.

Inconsistency of Minimum Variance Quadratic Unbiased Estimators under Non-Gaussian Compound Normal Distribution

Inconsistency of Minimum Variance Quadratic Unbiased Estimators under Non-Gaussian Compound Normal Distribution